Tim Olson
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58 lines
3.0 KiB
Markdown
58 lines
3.0 KiB
Markdown
---
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description: "Signals long/short entries when a shorter moving average crosses above or below a longer moving average, optionally augmented with stop-loss rules based on price thresholds."
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tags: [stocks, trend-following, moving-average, technical-analysis]
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---
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# Two Moving Averages
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**Section**: 3.12 | **Asset Class**: Stocks | **Type**: Trend-Following / Technical Analysis
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## Overview
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The two-moving-averages strategy replaces the current stock price in the single-MA signal with a shorter moving average. When the shorter MA crosses above the longer MA, a long position is established (bullish signal); when the shorter MA crosses below, a short position is established (bearish signal). This reduces sensitivity to single-day price noise relative to the single-MA strategy.
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## Construction / Signal
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Two MAs with lengths T' < T (e.g., T' = 10 days, T = 30 days):
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**Basic signal**:
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```
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Signal = { Establish long / liquidate short if MA(T') > MA(T)
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{ Establish short / liquidate long if MA(T') < MA(T) (322)
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```
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**With stop-loss rules** (Delta is a predefined percentage threshold, e.g., Delta = 2%):
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Let P_1 be the previous day's closing price:
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```
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Signal = { Establish long position if MA(T') > MA(T)
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{ Liquidate long position if P < (1 - Delta) * P_1
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{ Establish short position if MA(T') < MA(T)
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{ Liquidate short position if P > (1 + Delta) * P_1 (323)
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```
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A long position is liquidated if the current price P falls more than Delta below the previous day's price P_1 (even if the shorter MA has not yet crossed the longer MA). Similarly, a short position is liquidated if P rises more than Delta above P_1.
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## Entry / Exit Rules
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- **Long entry**: MA(T') crosses above MA(T).
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- **Long exit**: MA(T') crosses below MA(T), or price falls Delta% below prior day's close (stop-loss).
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- **Short entry**: MA(T') crosses below MA(T).
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- **Short exit**: MA(T') crosses above MA(T), or price rises Delta% above prior day's close (stop-loss).
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## Key Parameters
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- **Short MA length T'**: Typically 10–50 trading days
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- **Long MA length T**: Typically 30–200 trading days; T' < T required
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- **MA type**: SMA or EMA for both
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- **Stop-loss threshold Delta**: Typically 1–3% (e.g., 2%)
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- **Example**: T' = 10, T = 30; or classic "golden cross" T' = 50, T = 200
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## Variations
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- **No stop-loss**: Use basic signal (Eq. 322) only
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- **EMA crossover**: Use exponential MAs instead of simple MAs for both T' and T
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- **Three moving averages**: See Section 3.13 for additional false-signal filtering
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## Notes
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- The two-MA crossover is a classic technical analysis signal (e.g., "golden cross": 50-day MA crosses 200-day MA bullishly).
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- Stop-loss rules protect realized profits but can trigger premature exits if the shorter MA has not yet crossed.
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- Like all single-stock technical analysis strategies, this is considered "unscientific" by many academics but is widely used in practice.
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- Applicable on a single-stock or multi-stock basis.
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- Delta must be calibrated via backtesting; too tight a stop causes excessive whipsaw, too loose provides little protection.
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